PLEASE HELP MEEE :( consider the points P (-3, 0), Q (a, b) R (3, -3) and S (b+2,a+5). find the coordinates of Q and S if figure PQRS forms a parallelogram.
okay so what i did is equate the slope and distances of lines PQ and RS... but i'm still not getting a final answer :(

- anonymous

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- anonymous

slope pq= slope rs--> b/(a+3)=(a+8)/(b-1)
distance pq = distance rs --> (a+3)^2+b^2=(b-1)^2+(a+8)^2 so b=5a+28
tried to do systems but then there's no answer?!?!?! based on http://www.wolframalpha.com/input/?i=%28a%2B3%29%5E2%2Bb%5E2%3D%28b-1%29%5E2%2B%28a%2B8%29%5E2%3B+b%2F%28a%2B3%29%3D%28a%2B8%29%2F%28b-1%29 huhuhu someone help please :((

- anonymous

did you try solving it with vectors?

- amistre64

im thinking of midpoints :)

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## More answers

- amistre64

(P+R)/2 = (Q+S)/2
P+R = Q+S

- amistre64

but that just gets me parallel lines that have no solution :/
a+b = -2
a+b = -8

- amistre64

is there a figure to pull information off of?

- amistre64

|dw:1345725961534:dw|
we need to develop a notion of the rule that defines Q and S to narrow down the options eh

- anonymous

what did you mean by your last message, amistre64? btw, is there anything wrong with my solution?

- amistre64

a parallelagram is defined as opposite sides are parallel; i was just looking for "orbits" that would define the possibilities of 2 other points.

- anonymous

ghass1978, nope i don't remember how to use vectors... it's not part of our exam. sorry

- amistre64

your initial ideas look good in that they are defining valid properties

- amistre64

is there a diagram that goes with this? or is it just a wordy problem?

- anonymous

just that, exactly that :( waaaaahhh :(

- anonymous

but it says PQRS which means the sequence of the coordinates would be that way. as in Q "between" P and R... if that's what you're wondering

- amistre64

|dw:1345726700410:dw|
without using the relationship between Q and S, we can get any number of values for Q and S

- amistre64

Q(0,0) S(2,5) if we adjust this so that the midpoint is at 0,-1.5 it satisfies the rule
Q(-1,-4) S(1,1) is a solution

- anonymous

wait wait i don't get your drawing??? how did you get those? :( sorry!! i don't think we were taught that method yet?

- anonymous

why get the midpoint?

- amistre64

draw a parallelgram|dw:1345727410942:dw|

- amistre64

|dw:1345727435579:dw||dw:1345727448036:dw|

- amistre64

the midpoint of PR is the midpoint of QS , define some points that match the rule
Q(a,b) S(b+2,a+5)
and resolve the midpoint by moving the points about

- amistre64

any scaled values of Q and S also work
if there is a given picture to conform to, we can narrow down the odds of what they want tho

- amistre64

|dw:1345727657560:dw|

- SWAG

Nice work @amistre64

- amistre64

thnx :)

- anonymous

the right answer is S(5, -4) and Q(-9,3) ?? just found out now... how do you get that then? btw i will close this, have another question to ask.

- amistre64

-9, 3
5,-4
------
-4,-1 ; midpoint = -2,-1/2
-3, 0
3, -3
------
0,-3 ; midpoint = 0, -3/2
you either have some misinformation in the post, or the answer is wrong.

- anonymous

okay wait so i did the midpoint thing but i'm still lost...
midpoint of pr is (0, -3/2)
midpoint of qs is ([a+b+2]/2, [a+b+5]/2)
i tried equating [a+b+2]/2=0 and [a+b+5]/2=-3/2 then i got...
a+b=-2
a+b=-8
??? so how did you get Q(-1,-4) S(1,1) ?

- anonymous

nevermind, i believe our teacher gave the wrong given. i believe s should have been (a+2, b+5)

- amistre64

I essentially created a set of points in a different place that matched the given rule. Then I moved those points into the proper position.

- amistre64

using your new rule for Q and S ....
Q(a,b) S(a+2, b+5)
select any values you want for a and b; say a=6 and b=-1 .... random picks
Q(6,-1) S(6+2, -1+5)
Q(6,-1) S(8, 4)
now that I have a set of points that matches the rule, lets determine its own midpoint as is
(7 , 3/2)
now i want this midpoint to be at (0,-3/2), so lets see how we adjust it to get there
(7 , 3/2)
-7, -6/2 <---- i need to move Q and S by the same
--------
(0, -3/2)
since we have to move the midpoint by (-7,-3), we will have to move Q and S by the same amount
Q(6,-1) S(8, 4)
-7 -3 -7 -3
------- --------
Q(-1,-4) S(1, 1)
now we have a set of points Q and S that match the given rule; and is located in the proper spot

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